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  • Need solution for rd sharma maths class 12 chapter Indefinite Integrals exercise 18.2 question 22

Solution:  We have , 

  I=\int (\sec^{2}x+\cos ec^{2}x)dx\\ \\ \Rightarrow \hspace{1cm}I=\tan x -\cot x+c

Answers (1)

tan x-cot x+c

Hint: To solve this equation we use \int sec^{2} x dx and \int \cos ec^{2} xdx formula

\begin{aligned} &\text { Given: } \int \sec ^{2} x+\cos e c^{2} x d x \\ &\text { Solution: } \int \sec ^{2} x+\cos e c^{2} x d x \\ &=\int \sec ^{2} x d x+\int \cos e c^{2} x d x \quad\left[\begin{array}{l} \int \sec ^{2} x d x=\tan x+c \\ \int \operatorname{cosec}^{2} x d x=\cot x+c \end{array}\right] \\ &=\tan x-\cot x+c \end{aligned}

 

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